Mitt Romney wants you to know that both of these things are true: 1) He remained the “controlling person” in a number of Bain Capital investments between 1999 and 2002, when he left to work on the Salt Lake City Olympics. 2) He had no actual personal control over those investments during that time.

This is not a particularly comfortable position for a presidential candidate to be in, though it is also not exactly an unusual one for Romney, who has, among other things, both taken credit for President Obama’s bailout of Detroit and opposed Obama’s bailout of Detroit.

Statement No. 1 comes in several contemporaneous SEC filings, which the Obama campaign has been sending around to reporters. Statement No. 2 comes from Mitt Romney and Bain Capital and was certified on a federal financial disclosure in 2011, when Romney said he left active management of Bain Capital to work on the Olympics in 1999. That means Romney’s position is that he was the “controlling person” and yet had no active management responsibilities.

On top of this complex argument, which even a Romney campaign aide admits does not “square with common sense,” the Obama campaign has tried to set off the campaign equivalent of a bunker buster. In a conference call Thursday morning, Obama campaign senior adviser Stephanie Cutter put it this way:

Either Mitt Romney, through his own words and his own signature, was misrepresenting his position at Bain to the SEC, which is a felony, or he was misrepresenting his position at Bain to the American people to avoid responsibility for some of the consequences of his investments.

So Mitt Romney is either a crook or a liar, says Team Obama. There is a third possibility, which is that the SEC filings Romney submitted describing himself as the “controlling person” in the investments did not legally require him to have any actual control. Other contemporaneous documents obtained by Fortune magazine show that Bain was telling investors at the same time as the SEC filings that Romney was not a manager of the funds in question. But good luck putting that in a campaign ad.

Instead, the Romney campaign has responded to the Obama bunker buster with ordnance of its own. In a statement to reporters, Romney campaign manager Matt Rhoades demanded that Cutter apologize for calling Romney a potential crook.

President Obama’s campaign hit a new low today when one of its senior advisers made a reckless and unsubstantiated charge to reporters about Mitt Romney that was so over the top that it calls into question the integrity of their entire campaign. President Obama ought to apologize for the out-of-control behavior of his staff, which demeans the office he holds. Campaigns are supposed to be hard fought, but statements like those made by Stephanie Cutter belittle the process and the candidate on whose behalf she works.

In other words, Rhoades is arguing that only a crook would call Mitt Romney a crook and that Obama will have to deal with the fact that there are crooks in his campaign. Stay tuned for more.

UPDATE: More came quickly. The Huffington Post acquired testimony Romney gave in 2002 to the Ballot Law Commission in Massachusetts, in which Romney said he had “remained on the board of the Staples Corporation and Marriott International, the LifeLike Corporation” and returned to the state for “board meetings, Thanksgiving and so forth” from 1999 to 2002. The Romney campaign says this does not contradict his claim that he had no control over Bain Capital during that time, since there is a difference between Bain Capital and the companies in which Bain had significant ownership stakes.

But again, this is a complex distinction. In 2011, Romney said he had “not been involved in the operations of any Bain Capital entity in any way” since February 1999. Presumably this means he does not consider the companies with which Bain invested, like Staples and LifeLike, to be Bain Capital entities.